Alexis Malaware
Ex-Soldier
I could argue that it's a translational error and just dodge a bullet that way... but I do kinda think it's as simple as "Cloud was a Grunt. He was a nobody, nobody (other than Zack in CC) knew who he was.. he didn't have a name." Sephiroth never said he wasn't given a name.. just that he didn't have one.
Sephiroth was lying to Cloud, period. Sephiroth even told Cloud that he wasn't there at Nibelheim (when he was and Sephiroth knew that as fact) that Cloud was nothing more than a cluster of Jenova cells, that he wasn't real, that he only taken on the memories of a boy named Cloud. Hence never having a name because Sephiroth is implying that he's not real in the first place, to break his mind.